Finite Group Databasebeta

← C3×#73440 #11801925

Subgroups — C3×#73440 #11801925

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C32×C4×C22⋊C4C211yesmaximal, characteristic
3C3×C4×#217C211yesmaximal, characteristic
4C3×#4945C212yesmaximal
5C3×#4944C212yesmaximal
6C3×#4932C211yesmaximal, characteristic, complemented
7C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
8C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
9C3×C42×Dic3C211yesmaximal, characteristic, complemented
10C3×#4654C212yesmaximal, complemented
11C3×#4653C212yesmaximal, complemented
12C3×#2298—31nomaximal
13#73440C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2211yescharacteristic
15C2×C32×C22⋊C4C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×C3×#217C2212yes—
19C2×C3×#217C2211yescharacteristic
20C2×C3×#217C2211yescharacteristic
21C3×#926C418yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C32×#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×#117—31no—
39C2×#926C2×C311yescharacteristic
40C3×#388—32no—
41C3×#388—32no—
42C3×#387—32no—
43C3×#387—32no—
44C3×C4×C4⋊C4—31no—
45C3×C4×C4⋊C4—31no—
46C3×C4×C22⋊C4—21no—
47C3×C4×C22⋊C4—31no—
48C3×C4×C22⋊C4D311yescharacteristic
49C3×C4×C22⋊C4C2×C311yescharacteristic
50C3×#376—31no—
51C3×C43—31no—
52C4×#217C2×C311yescharacteristic
53#4945C2×C312yes—
54#4944C2×C312yes—
55#4932C2×C311yescharacteristic, complemented
56C4×Dic3⋊C4C2×C311yescharacteristic, complemented
57C4×Dic3⋊C4C2×C311yescharacteristic, complemented
58C42×Dic3C2×C311yescharacteristic, complemented
59#4654C2×C312yescomplemented
60#4653C2×C312yescomplemented
61C24×C32C2311yescharacteristic
62C22×C32×C4—22no—
63C22×C32×C4—22no—
64C22×C32×C4C2×C414yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C32×C22⋊C4—24no—
76C32×C42—22no—
77C32×C42—22no—
78C3×#217—24no—
79C3×#217C2×C414yes—
80C3×#217C2×C414yes—
81C3×C4⋊Dic3C2×C414yes—
82C3×C4⋊Dic3C2×C414yes—
83C3×Dic3⋊C4—24no—
84C3×Dic3⋊C4—24no—
85C3×C4×Dic3—24no—
86C3×C4×Dic3—22no—
87C3×C4×Dic3—22no—
88C3×C4×Dic3—24no—
89C3×C4×Dic3C2×C414yes—
90C3×C4×Dic3C2×C414yes—
91#2298—31noSylow
92C23×C3×C4—21no—
93C23×C3×C4C2×D311yescharacteristic
94C23×C3×C4C22×C311yescharacteristic
95C3×#117—38no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4—31no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C22⋊C4C2×D312yes—
105C2×C3×C22⋊C4C22×C312yes—
106C2×C3×C42—21no—
107C2×C3×C42—21no—
108C2×C3×C42—31no—
109C2×C3×C42—31no—
110C2×C3×C42—32no—
111C2×C3×C42—32no—
112C2×C3×C42—31no—
113C2×C3×C42—31no—
114C2×C3×C42C2×D311yescharacteristic
115C2×C3×C42C2×D311yescharacteristic
116C2×C3×C42C22×C311yescharacteristic
117C2×C3×C42C22×C311yescharacteristic
118C2×#217C22×C312yes—
119C2×#217C22×C311yescharacteristic
120C2×#217C22×C311yescharacteristic
121#926C3×C418yescomplemented
122C2×C4⋊Dic3C22×C311yescharacteristic
123C2×C4⋊Dic3C22×C311yescharacteristic
124C2×Dic3⋊C4C22×C312yes—
125C2×Dic3⋊C4C22×C312yes—
126C2×C4×Dic3C22×C312yes—
127C2×C4×Dic3C22×C312yes—
128C2×C4×Dic3C22×C311yescharacteristic
129C2×C4×Dic3C22×C311yescharacteristic
130C2×C4×Dic3C22×C311yescharacteristic
131C2×C4×Dic3C22×C311yescharacteristic
132C3×#95—22no—
133C3×#95—32no—
134C3×#95—32no—
135C3×#95—32no—
136C3×#95—32no—
137C3×#95—32no—
138C3×#95C2×D312yes—
139C3×#95C22×C312yes—
140C3⋊#95C22×C312yes—
141C3⋊#95C22×C312yes—
142C3⋊#95C22×C312yes—
143C3⋊#95C22×C312yes—
144C3⋊#95C22×C312yes—
145C23×C32—22no—
146C23×C32—22no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32C22×C412yes—
150C23×C32C2411yescharacteristic
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—28no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4C22×C412yes—
160C2×C32×C4C22×C412yes—
161C2×C32×C4#4114yes—
162C2×C32×C4#4112yes—
163C2×C32×C4#4112yes—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3#4114yes—
178C2×#117—31no—
179#388—32no—
180#388—32no—
181#387—32no—
182#387—32no—
183C4×C4⋊C4—31no—
184C4×C4⋊C4—31no—
185C4×C22⋊C4—31no—
186C4×C22⋊C4C3×D311yescharacteristic
187#376—31no—
188C43—31no—
189C24×C3—21no—
190C24×C3C22×D311yescharacteristic
191C24×C3C23×C311yescharacteristic
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—24no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—32no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—42no—
208C22×C3×C4—42no—
209C22×C3×C4C4×D314yes—
210C22×C3×C4C2×C3×C414yes—
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D312yes—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C23×C312yes—
216C22×C3×C4C23×C311yescharacteristic
217C22×C3×C4C23×C312yes—
218C22×C3×C4C23×C311yescharacteristic
219C22×Dic3C23×C312yes—
220C22×Dic3C23×C311yescharacteristic
221C22×Dic3C23×C311yescharacteristic
222C22×Dic3C23×C311yescharacteristic
223C22×Dic3C23×C311yescharacteristic
224C22×Dic3C23×C312yes—
225C3×C4⋊C4—34no—
226C3×C4⋊C4—34no—
227C3×C4⋊C4—64no—
228C3×C4⋊C4—64no—
229C3×C22⋊C4—28no—
230C3×C22⋊C4—24no—
231C3×C22⋊C4—24no—
232C3×C22⋊C4—34no—
233C3×C22⋊C4—34no—
234C3×C22⋊C4—64no—
235C3×C42—22no—
236C3×C42—22no—
237C3×C42—22no—
238C3×C42—22no—
239C3×C42—34no—
240C3×C42—34no—
241C3×C42—42no—
242C3×C42—42no—
243C3×C42—64no—
244C3×C42—64no—
245C3×C42—62no—
246C3×C42—62no—
247#217—24no—
248#217C2×C3×C414yes—
249#217C2×C3×C414yes—
250C4⋊Dic3C2×C3×C414yes—
251C4⋊Dic3C2×C3×C414yes—
252Dic3⋊C4—24no—
253Dic3⋊C4—24no—
254C4×Dic3—24no—
255C4×Dic3—22no—
256C4×Dic3—22no—
257C4×Dic3—24no—
258C4×Dic3C2×C3×C414yes—
259C4×Dic3C2×C3×C414yes—
260C22×C32—22no—
261C22×C32—22no—
262C22×C32—22no—
263C22×C32—42no—
264C22×C32—42no—
265C22×C32C23×C411yescharacteristic
266C22×C32C2×#4112yes—
267C22×C32C2×#4111yescharacteristic
268C22×C32C2×#4111yescharacteristic
269C22×C32C2×#4112yes—
270C32×C4—22no—
271C32×C4—24no—
272C32×C4—42no—
273C32×C4#11714yes—
274C3×Dic3—22no—
275C3×Dic3—22no—
276C3×Dic3—22no—
277C3×Dic3—22no—
278C3×Dic3—24no—
279C3×Dic3—42no—
280C23×C4C2×C3×D311yescharacteristic
281#117—38no—
282C2×C4⋊C4—31no—
283C2×C4⋊C4—31no—
284C2×C4⋊C4—32no—
285C2×C4⋊C4—32no—
286C2×C22⋊C4—31no—
287C2×C22⋊C4—31no—
288C2×C22⋊C4—32no—
289C2×C22⋊C4C2×C3×D312yes—
290C2×C42—31no—
291C2×C42—31no—
292C2×C42—31no—
293C2×C42—32no—
294C2×C42—32no—
295C2×C42—31no—
296C2×C42C2×C3×D311yescharacteristic
297C2×C42C2×C3×D311yescharacteristic
298#95—32no—
299#95—32no—
300#95—32no—
301#95—32no—
302#95—32no—
303#95C2×C3×D312yes—
304C23×C3—24no—
305C23×C3—22no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—22no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—42no—
318C23×C3C2×C4×D312yes—
319C23×C3C22×C3×C412yes—
320C23×C3C23×D311yescharacteristic
321C23×C3C24×C311yescharacteristic
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—28no—
331C2×C3×C4—28no—
332C2×C3×C4—24no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—24no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—34no—
349C2×C3×C4—48no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4C2×C4×D312yes—
366C2×C3×C4C2×C4×D312yes—
367C2×C3×C4#23514yes—
368C2×C3×C4#23712yes—
369C2×C3×C4#23712yes—
370C2×C3×C4C22×C3×C412yes—
371C2×C3×C4C22×C3×C412yes—
372C2×C3×C4C3×#4114yes—
373C2×C3×C4C3×#4112yes—
374C2×C3×C4C3×#4112yes—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3C22×C3×C412yes—
385C2×Dic3C22×C3×C412yes—
386C2×Dic3C22×C3×C412yes—
387C2×Dic3C22×C3×C412yes—
388C2×Dic3C3×#4114yes—
389C2×C32—42no—
390C2×C32C2×#11711yescharacteristic
391C2×C32C4×#4111yescharacteristic
392C2×C32C4×#4111yescharacteristic
393C2×C32#52912yes—
394C2×C32#52912yes—
395C24C22×C3×D311yescharacteristic
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—31no—
399C22×C4—31no—
400C22×C4—32no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—32no—
404C22×C4C3×C4×D314yes—
405C22×C4C22×C3×D312yes—
406C22×C4C22×C3×D311yescharacteristic
407C22×C4C22×C3×D312yes—
408C22×C4C22×C3×D311yescharacteristic
409C4⋊C4—34no—
410C4⋊C4—34no—
411C4⋊C4—64no—
412C4⋊C4—64no—
413C22⋊C4—24no—
414C22⋊C4—34no—
415C22⋊C4—34no—
416C22⋊C4—64no—
417C42—22no—
418C42—22no—
419C42—34no—
420C42—34no—
421C42—64no—
422C42—64no—
423C42—62no—
424C42—62no—
425C22×C3—24no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—22no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—44no—
440C22×C3—44no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3C22×C4×D311yescharacteristic
446C22×C3C2×#23512yes—
447C22×C3C2×#23711yescharacteristic
448C22×C3C2×#23711yescharacteristic
449C22×C3D3×#4112yes—
450C22×C3C23×C3×C411yescharacteristic
451C22×C3C2×C3×#4112yes—
452C22×C3C2×C3×#4111yescharacteristic
453C22×C3C2×C3×#4111yescharacteristic
454C22×C3C2×C3×#4112yes—
455C3×C4—22no—
456C3×C4—24no—
457C3×C4—22no—
458C3×C4—24no—
459C3×C4—24no—
460C3×C4—42no—
461C3×C4—44no—
462C3×C4—44no—
463C3×C4—42no—
464C3×C4—42no—
465C3×C4—62no—
466C3×C4—62no—
467C3×C4—62no—
468C3×C4—62no—
469C3×C4—64no—
470C3×C4—122no—
471C3×C4#87714yes—
472C3×C4C3×#11714yes—
473Dic3—22no—
474Dic3—22no—
475Dic3—22no—
476Dic3—22no—
477Dic3—24no—
478Dic3—42no—
479C32#229811yescharacteristic, complemented, Sylow
480C23—22no—
481C23—21no—
482C23—21no—
483C23—22no—
484C23C2×C3×C4×D312yes—
485C23C23×C3×D311yescharacteristic
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—28no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—34no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4C2×C3×C4×D312yes—
509C2×C4C2×C3×C4×D312yes—
510C2×C4C3×#23514yes—
511C2×C4C3×#23712yes—
512C2×C4C3×#23712yes—
513C2×C3—21no—
514C2×C3—22no—
515C2×C3—22no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—44no—
519C2×C3—42no—
520C2×C3—42no—
521C2×C3C4×#23511yescharacteristic
522C2×C3C2×#87711yescharacteristic
523C2×C3#552211yescharacteristic
524C2×C3#553812yes—
525C2×C3#555712yes—
526C2×C3C2×C3×#11711yescharacteristic
527C2×C3C3×C4×#4111yescharacteristic
528C2×C3C3×C4×#4111yescharacteristic
529C2×C3C3×#52912yes—
530C2×C3C3×#52912yes—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—42no—
535C22—42no—
536C22C22×C3×C4×D311yescharacteristic
537C22C2×C3×#23512yes—
538C22C2×C3×#23711yescharacteristic
539C22C2×C3×#23711yescharacteristic
540C22C3×D3×#4112yes—
541C4—24no—
542C4—22no—
543C4—42no—
544C4—62no—
545C4—62no—
546C4—64no—
547C4—62no—
548C4—62no—
549C4—122no—
550C4C3×#87714yes—
551C3—21no—
552C3#7344011yescharacteristic, direct product factor
553C3C3×#229811yescharacteristic, complemented
554C2—42no—
555C2C3×C4×#23511yescharacteristic
556C2C2×C3×#87711yescharacteristic
557C2C3×#552211yescharacteristic
558C2C3×#553812yes—
559C2C3×#555712yes—
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×C4×C22⋊C4C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×#2298
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
6. C3×#4932C2semidirect
7. C3×C4×Dic3⋊C4C2semidirect
8. C3×C4×Dic3⋊C4C2semidirect
9. C3×C42×Dic3C2semidirect
10. C3×#4654C2semidirect
11. C3×#4653C2semidirect
13. #73440C3direct (N × H)
21. C3×#926C4semidirect
55. #4932C2×C3semidirect
56. C4×Dic3⋊C4C2×C3semidirect
57. C4×Dic3⋊C4C2×C3semidirect
58. C42×Dic3C2×C3semidirect
59. #4654C2×C3semidirect
60. #4653C2×C3semidirect
121. #926C3×C4semidirect
479. C32#2298semidirect
552. C3#73440direct (N × H)
553. C3C3×#2298semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#9262
C32×C4×C22⋊C42
C3×C4×#2172
C3×#49452
C3×#49442
C3×#49322
C3×C4×Dic3⋊C42
C3×C42×Dic32
C3×#46542
C3×#46532
C3×#22983
#734403